Luke 1:59

59. They came To the house probably of Zacharias. For no particular place was prescribed, and no particular person as performer of the rite.

To circumcise the child Circumcision was given by God to Abraham as the sign of the covenant between God and the circumcised. Perhaps it was, as in the case of sacrifices, merely the renewal of an ancient rite, for we find that not only the Jews and other Abrahamic tribes practised the rite, but the Ethiopians, Abyssinians, Egyptians, and others. Under the Mosaic law, infant circumcision was the rite of induction into the kingdom of God. It was the condition to be performed before the adult person could partake of the paschal feast. Exodus 12:43-48. This was enjoined with great solemnity. So under the Christian dispensation except a man be externally born of water he cannot see the external kingdom of God. John 3:3. That is, as circumcision once, so baptism now is the admission rite of the Church of God. From this it would follow that no one who is not qualified if an adult, by justifying faith, if an infant, by the unconditional power of the atonement to enter the kingdom of God, is qualified for baptism. And as circumcision was required previous to the paschal feast, so baptism should be performed previous to the partaking of the communion.

They called him The name was generally given to the child by the Jews at circumcision. Like baptism, circumcision was the sacred recognition of the personality of the individual; and the persons solemnly present are proper witnesses to identify him in case of future dispute. So in our old English, to baptize is to christen, that is, both to Christianize and to name him; giving him his Christian or christen name.